Is someone who says "I am an unbeliever" with the intention of silencing her father, who described her prayer as "useless," considered an unbeliever, even though she did not intend to disbelieve in Allah?

Anger does not preclude accountability unless one loses their mind with it and the angry person no longer comprehends what they are saying. The majority of jurists hold that an angry person is still accountable and responsible for what they say or do. The statement "I am an unbeliever (kafirah)" is a dangerous phrase, and whoever utters it willingly has committed an act of disbelief (kufr) by doing so, unless there is an interpretative justification for it. Therefore, one must repent to Allah for what was said.